P1252428721XqySY

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Integrated GPS/INS System in Support of Direct
Geo-referencing Dorota A. Grejner-Brzezinska Ci
vil and Environmental Engineering and Geodetic
Science The Ohio State University 470 Hitchcock
Hall Columbus, OH 43210 Tel. (614)
292-8787 E-mail dorota_at_cfm.ohio-state.edu
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Presentation outline

• Direct georeferencing concept
• GPS/INS integration for positioning and
  orientation
• INS component
• GPS component
• Primary integration architectures
• Summary

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Georeferencing the Concept (1)

• Sensor orientation, also called image
  georeferencing, is defined by a transformation
  between the image coordinates specified in the
  camera frame and the geodetic (mapping) reference
  frame.
• requires knowledge of the camera interior and
  exterior orientation parameters (EOP)
• interior orientation principal point
  coordinates, focal length, and lens geometric
  distortion are provided by the camera calibration
  procedure
• exterior orientation spatial coordinates of the
  perspective center, and three rotation angles
  known as ?, ?, and ?

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Georeferencing the Concept (2)

• Traditional aerial surveying
• EOP determined from the aerotriangulation,
  defining correlation between ground control
  points and their corresponding image
  representations
• requires scene pre-targeting
• high cost
• labor intensive

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Georeferencing the Concept (3)

• Modern aerial surveying
• EOP determined directly from integrated sensors
  such as GPS/INS or GPS antenna array
• no scene pre-targeting (no ground control,
  except for GPS base station)
• no aerotriangulation
• low cost
• allows automation of the data image processing

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Automation of Aerial Survey

• System augmentation by an inertial sensor offers
  a number of advantages over a stand-alone GPS
• immunity to GPS outages
• continuous attitude solution
• reduced ambiguity search volume/time
• high accuracy and stability over time
  contributed by GPS, enabling a continuous
  monitoring of inertial sensor errors
• Result ? direct platform orientation
  (geo-referencing)

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Direct Geo-referencing

• Increased interest in the aerial survey and
  remote sensing community
• need to accommodate the new spatial data sensors
  (LIDAR, SAR, multi/hyperspectral)
• cost reduction of aerial mapping
• decreased need for control points
• maturity and cost-effectiveness of GPS/INS
  systems
• GPS multi-antenna systems for less demanding
  applications
• GPS/INS systems available
• experimental - University of Calgary, Center for
  Mapping OSU
• commercial - Applanix

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Direct Orientation Airborne System
INS Position Attitude (x, y, z) and (?, ?, ?)
GPS Position Time (x, y, z)
Imaging Stereo Digital Images
Digital Elevation Model
Digital Orthophoto
Hypsography Hydrography
Topography
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Direct Orientation Land-based System
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• For precise spatial positioning

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Direct Orientation Land-based System
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Direct Orientation Airborne System
GPS Antenna
INS
PC
Two Base Stations
Camera
GPS Receiver
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Direct Georeferencing
YBINS
XBINS
XC
YC
ZBINS
ZM
rM,INS
rm,i,j

• 3D INS coordinates in mapping frame
• 3D object coordinates in model frame (derived
  from i,j stereo pair) attached to C-frame
• 3D coordinates of point k in M-frame
• boresight matrix between INS body frame and
  camera frame C
• rotation matrix between INS body frame and
  mapping frame M, measured by INS
• boresight offset components
• scaling factor

rM,INS rm,i,j rM,k
YM
rM,k
XM
s
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GPS/INS Integration for Direct Orientation
(direct geo-referencing) of the Imaging Component
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Principles of Inertial Navigation

• Principles defined in the i-frame (inertial)
• Real time indication of position and velocity of
  a moving vehicle using sensors that react on the
  basis of Newtons laws of motion
• these sensors are called Inertial Measurement
  Units (IMU)
• accelerometers
• sense linear acceleration in inertial frame
• does not sense the presence of a gravitational
  field
• gyroscopes (sense rotational motion)
• facilitate the rotation between navigation and
  INS body frames (in fact rotation with respect to
  the inertial frame is measured)
• Integration with respect to time of the sensed
  acceleration to obtain velocity, and subsequent
  integration to obtain position

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Coordinate Frame Geometry
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Inertial Navigation System (INS)

• Provides self-contained independent means for
  3-D positioning
• Three gyros and three accelerometers (or less)
• Accuracy degrades exponentially with time due to
  unbounded positioning errors caused by
• uncompensated gyro errors
• uncompensated accelerometer errors
• fast degradation for low cost INS
• High update rate (up to 256 Hz)
• Mechanical (stabilized platform) systems
• sense acceleration in inertial frame
  coordinatized in navigation frame
• Strapdown systems (digital)
• sense acceleration in inertial frame
  coordinatized in body frame

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INS LN-100 Body Axes
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Primary Error Sources

• The main sources of errors in an inertial
  navigation are due to the following factors
• The time rates of change of the velocity errors
  are driven chiefly by accelerometer errors and
  gravity anomalies
• The attitude error rates are driven primarily by
  gyroscope errors
• Three basic classes of errors
• physical component error deviation of inertial
  sensors from their design behavior (drifts, bias,
  scaling factors)
• construction errors errors in overall system
  construction such as mechanical alignment errors
• initial conditions errors that arise from
  imperfect determination of the initial position
  error, initial velocity error, and initial
  platform misalignment

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Comparison of GPS and INS Free Navigation
Trajectories (Road Test)
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Strapdown INS

• Strapdown system algorithms are the mathematical
  definitions of processes, which convert the
  measured outputs of IMUs that are fixed to the
  vehicle body axis, into quantities that can be
  used to control the vehicle (attitude, velocity
  and positions)
• The outputs are angular rates and linear
  velocities along the orthogonal axes
• The measured angular rates are converted into
  changes in attitude of the vehicle with respect
  to its initial orientation
• The resulting attitude transformation matrix is
  used to convert the measured velocities from body
  axes to the reference coordinate system
• The major algorithms are
• Start-up
• Initialization
• Generation of the transformation algorithm
• Navigation

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Strapdown INS

• Start-up
• the operational readiness is determined
  immediately after the power is turned on, by
  buit-in stimuli-response go/no go tests
• this tests isolate system faults to a single
  gyro or accelerometer or control electronics
• Initialization
• as a dead reckoning device, it INS must know the
  initial conditions of the position and velocity
  from the external source
• direction of the initial velocity vector is
  determined by the process of alignment
• may include self-calibration

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Initial Alignment

• Process of initially locating the sensitive axes
  of the accelerometers with respect to the
  reference or navigation coordinate system axes
  (transformation matrix)
• can be autonomous (without recourse to other
  equipment)
• self-leveling in the stationary mode it is
  accomplished by initial computation of the
  direction cosine transformation matrix to
  force the transformed velocity to have zero
  components in the horizontal reference directions
• gyrocompassing closed-loop process of locating
  true North by computing heading as an element of
  the transformation matrix that has been initially
  leveled (analogous to torquing the gimbals until
  the East gyro angular rate measurement is nulled)
• can measure total drift rate about the vertical
  axes by recursive solution (self-calibration)
• or slaved (by matching the starpdown system
  outputs to some external system

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Strapdown INS Alignment

• Coarse Alignment
• For stationary system utilizes the gravity and
  earth rotation vectors as well as accelerometer
  and gyro outputs to determine the initial
  estimate of the transformation matrix (no sensor
  errors assumed)

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Coarse Self-Alignment Using Analytic Alignment
Scheme
Determination of pitch angle q and the roll
angle f
time interval D T
Determination of azimuth angle y
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Strapdown INS Alignment

• Self-Corrective Alignment
• because an initial estimate of the
  transformation matrix is available from the
  initial (coarse) alignment, the misalignment
  between the body and navigation frames can be
  modeled as a small angle rotation
• the updating method consists of detecting error
  angles between these two frames via the processed
  accelerometer and gyro signals and generating a
  signal to the transformation computer in order to
  drive these angles as close to zero as possible
• at the same time compensation is provided for
  the disturbance angular vibration

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Alignment (Optimal Estimator)
n
n
D
V
D
V
ib
nb
n
Known Velocity
C
_
b


_
_
b
D
q
nb
_

_

_
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Attitude Determination

• Euler method
• heading,pitch and roll, not suitable for
  strapdown system because the differential
  equations for their propagation contain
  trigonometric terms with singularities
• nonlinear differential equations
• Direction cosine method (DCM)
• differential equations for DCM propagation are
  linear and very simple
• the main disadvantage of DCM is that it has too
  many elements to be integrated
• computational burden
• Quaternion method

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Attitude Determination

• Quaternion method
• quaternion Q is a quadruple of real numbers, Q
  q0q1iq2jq3k that evolve in accordance with a
  simple differential equation and are only one
  more in number than the minimum number required
• three components define the axis of rotation,
  the fourth one the amount of rotation
• numerically stable characteristics
• can be converted to direction cosines and Euler
  angles
• preferred for strapdown systems

?b, ?n are skew-symmetric matrices containing the
rotation rates of the body-fixed frame w.r.t.
inertial frame in body-fixed coordinates
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Rotation Axis of Vector about which System a is
Rotated in Order to Coordinate with System b
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Error Sources in Numerical Solution (critical
for updating transformation matrix)

• Commutation errors
• result from fixed-sequence numerical processing
  in the strapdown algorithm
• can be minimized by increasing the update rate
• Integration errors
• due to discrete approximate solution of a
  continuous process
• can be minimized by implementing sophisticated
  algorithms and increasing the update rate
• Round-off errors
• due to finite resolution of data
• can be minimized by using double precision for
  critical operations
• Quantization errors
• analog-to-digital conversion of sensor measured
  outputs
• can be minimized by increased storage hardware
  and mathematical modeling

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Navigation Equations

• A general navigation equation that describes the
  motion of a point mass over the surface of the
  earth

f - acceleration due to applied force sensed by
accelerometer g(r) - gravitational acceleration r
geocentric vector of vehicle position v(t)
velocity of the vehicle relative to the earth
defined in the navigation system
- earth rotation vector
- angular rate of the navigation frame relative
to the earth
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Navigation Equations (cont)

• the Earths rotation rate L is the geodetic
  latitude, and l is the longitude.

- the direction cosine matrix from body-fixed
coordinates (b-frame) to navigation coordinates
(n-frame)

• the superscript n means a vector is
  coordinated in the n-frame

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Strapdown Inertial Mechanization
Position Velocity
n
n
D
V
D
V
ib
nb
Body-Mounted Accelerometers
n
C
b

_
Gravity Computation
Transformation Matrix Computation
Attitude
Euler Angle Computation
b
D
q
nb
b
Earth and Vehicle Rate Computation
b
D
q
D
q
ib
Body-Mounted Gyroscopes
in
_

b
D
V


Delta velocity from accelerometers

ib
b
Dq


Delta q from gyros (angular rates)
ib
n
C


Direction cosine matrix from b-frame to n-frame
b
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Why GPS/INS Integration?

• GPS and INS have complementary operational
  characteristics
• GPS contributes its white error spectrum, high
  accuracy and stability over time, enabling a
  continuous monitoring of inertial sensor errors
• Calibrated INS offers high short-term accuracy
  and high sampling rate
• INS is self-contained no outages
• GPS/INS offers a number of advantages over a
  stand-alone GPS
• immunity to GPS outages and reduced ambiguity
  search volume/time for the closed-loop systems
• and more importantly, continuous attitude
  solution
• Implementation of a closed-loop error
  calibration allows continuous, on-the-fly (OTF)
  error update bounding INS errors, leading to
  increased estimation accuracy
• Two primary integration modes
• Loose coupling
• Tight coupling (closed-loop)

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GPS/INS Integration

• Limitations
• High cost of high quality INS
• Mission objectives (what INS is needed and what
  can be afforded)
• How complex is the integration scheme required
  to achieve the emission objectives

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GPS/INS Integration

• Loosely coupled mode
• Separate filter to process GPS data
• IMU measurements are processed by inertial
  navigation and attitude algorithms to give
  inertial position, velocity, and attitude
  solution
• An integrated Kalman filter is then applied to
  combine the GPS and inertial solutions
• The main disadvantage positioning must be
  performed on the basis of IMU measurements alone
  when the number of tracked GPS satellites drops
  below four

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GPS/INS Integration

• Tightly coupled mode
• A single Kalman filter is designed to process
  both sets of sensor data raw GPS observations
  and IMU measurements
• OTF IMU error calibration by a feedback loop
• Allows use of GPS measurements from less than
  four satellites
• High accuracy of the inertial system over short
  periods of time allows correction of undetected
  cycle slips affecting GPS measurements
• Makes it possible to perform a faster and more
  robust OTF ambiguity resolution
• Offers a possibility to support GPS tracking
  loop by a direct feedback from the integrated
  filter to maintain tracking during high dynamics
• Offers superior performance compared to loosely
  coupled mode

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Computation Diagram for Loosely Integrated
GPS/INS System
CONTROL.DAT
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Architecture of Tightly Integrated GPS/INS System
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Summary Major Components of Integration
Algorithm and Filter Design

• Choice of coupling mode
• Number of states that should be estimated
• Whole-value filter states vs error states
• How often should the filter be updated
• How should the correlated measurements be
  treated
• How to reduce the computational burden by proper
  exploitation of the sparseness of the dynamics
  matrix
• How can the filter be used to detect the GPS or
  INS failure
• How can filter be made robust against varying
  error characteristics of INS or GPS

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Kalman Filter Model A using Linear INS Error
Model
INS Psi-Angle Error Model

• ?v, ?r, and ?? are the velocity, position, and
  attitude error vectors respectively
• is the accelerometer error vector
• ?g is the error in the computed gravity vector
• ? is the gyro drift vector.
• subscript b stands for bias
• subscript f stands for scaling factor

Example 24 INS States
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Kalman Filter Model BUsing Nonlinear State
Equation
Nonlinear State Equation

• v, r, and q are the velocity, position, and
  quaternion (associated with attitude
  determination) components
• subscript b stands for bias
• subscript f stands for scaling factor

Example 25 INS States